WORKING WITH NUMBERS
1
(a) In 2020, the running cost for Frederick’s car was $5200.
28% of the running cost was spent on insurance.
3
of the running cost was spent on maintenance.
25
$740 of the running cost was spent on tax.
The remainder of the running cost was spent on petrol.
(i) Calculate the amount Frederick spent on petrol.
[3]
(ii) In 2021, the tax increased by 1.5%.
[2]
Calculate the tax in 2021.
(b) In January, the cost of petrol is $2.20 per litre.
[1]
(i) Find the cost of 38.7 litres of petrol.
(ii) The average amount of petrol Frederick’s car uses is 7 litres per 100 km.
In January, he spends $215.60 on petrol.
[3]
Calculate the number of kilometres he drives in January.
(iii) In February, the cost of petrol increases to $2.24 per litre.
Calculate the percentage increase in the cost of petrol from January to February.
2
(a) The graph shows the cost, in dollars, of buying a length of fabric t metres long.
40
30
Cost ($) 20
10
0
0
1
2
3
Length of fabric (metres)
4
5 t
[2]
(i) Use the graph to find the cost of buying 3.8 m of fabric.
[1]
(ii) Samira buys k metres of fabric.
She pays with a $20 note and receives $1.50 change.
Use the graph to find the value of k.
[2]
(b) Anita cuts 10 m of fabric into three lengths to make a blouse, a skirt and a dress.
The lengths of fabric needed to make the blouse, the skirt and the dress are in the ratio 6 : 8 : 11.
Find the length of the fabric that is cut to make the dress.
[2]
(c) The upper bound for the area of a rectangular piece of fabric is 8.8125 m 2 .
The width of the piece of fabric is 2.3 metres, correct to the nearest 0.1 m.
The length of the piece of fabric is d metres, correct to the nearest 0.1 m.
Find the value of d.
3
[3]
(a) In 2021, the cost of posting a letter was 84 cents.
(i) A company posts 1950 letters. Find the cost, in dollars, to post these letters.
[1]
(ii) In 2022, the cost of posting a letter is 96 cents.
Calculate the percentage increase in the cost of posting a letter.
(b)
[2]
Cost of posting a letter is 96 cents
15% discount when monthly postage is more than $1000
Company A posts 1200 letters in one month.
Company B posts fewer letters than Company A in the same month.
Company A and Company B each pay the same amount to post their letters that month.
Find the number of letters Company B posts in that month.
[3]
(c) In 2022, the cost of posting a parcel with a mass of 1 kg or less is $4.60 .
The cost increases by $1.10 for each additional 0.5 kg.
Find the cost of posting a parcel with a mass of 3.5 kg.
[2]
(d) The cost of posting parcels increases by 7.2%.
After the increase, the cost of posting a parcel is $13.40 .
Calculate the original cost of posting this parcel.
[2]
4
(a) Abid works in an office for 5 days each week.
Each day he works from 08 15 until 12 40 and then from 13 30 until 17 00.
Work out the total time Abid works in one week.
Give your answer in hours and minutes.
[2]
(b) Abid earns $14.20 per hour.
He is given a pay increase of 5%.
[2]
Calculate the amount Abid earns per hour after the increase.
(c) Each month Abid divides his earnings between rent, bills and savings.
He uses 20% of his earnings for rent.
3
He uses of his earnings for bills.
8
The rest of his earnings are savings.
Find the ratio rent : bills : savings.
Give your answer in its simplest form.
[3]
(d) Abid invests $2400 in a savings account for 4 years.
The account pays simple interest at a rate of r % per year.
At the end of 4 years he receives a total of $153.60 in interest.
[2]
Calculate the value of r.
(e) Abid invests some money in a different savings account.
This account pays compound interest at a rate of 1.4% per year.
At the end of 5 years there is $1822.38 in the account.
[3]
Calculate the amount of money Abid invests in this account.
5
(a) Hala travels from London to Marseille by train.
She must change trains in Paris.
The journey from London to Paris takes 2 hours 28 minutes.
The journey from Paris to Marseille takes 3 hours 30 minutes.
The local time in Marseille and in Paris is 1 hour ahead of the local time in London.
(i) Complete the timetable for Hala’s journey.
Local time
London depart
Paris arrive
.........................
16 50
Local time
Paris depart
Marseille arrive
19 31
.........................
(ii) Work out how long Hala waits in Paris before the train to Marseille departs.
[2]
[1]
(b) The exchange rate between dollars ($) and pounds (£) is $1 = £0.75 .
The exchange rate between dollars ($) and euros (€) is $1 = €r.
Hala changes £250 into euros.
She receives €290.
Calculate the value of r.
[3]
(c) (i) Josef books a holiday for 3 people.
The holiday costs $420 per person.
Josef pays a deposit of 20% of the total cost of the holiday.
Calculate the amount Josef pays as the deposit.
[2]
(ii) Josef pays a total of $85.68 for airport parking for 8 days.
This price includes a reduction of 15% of the full price for booking early.
Calculate the full price for airport parking for 1 day.
6
[3]
(a) A machine makes five-cent coins.
It makes 720 coins per minute.
The machine operates for 24 hours per day.
Calculate the total value, in dollars, of the coins made by the machine in 300 days.
Give your answer in standard form, correct to 3 significant figures.
[3]
(b) The diameter of a five-cent coin is 21.2 mm, correct to the nearest 0.1 mm.
The diameter of a ten-cent coin is 17.9 mm, correct to the nearest 0.1 mm.
Marlon makes a line of 10 five-cent coins and a line of 10 ten-cent coins.
Calculate the upper bound of the difference between the lengths of the two lines.
7
[3]
In 2019 Nicole’s annual income was $22 000.
(a) She spent $7200 on accommodation in 2019.
Calculate the percentage of her income she spent on accommodation.
[2]
(b) Her annual income of $22 000 increased by 4% in 2020.
Calculate her annual income in 2020.
[2]
(c) Nicole invests $2000 in an account.
The account pays compound interest at a rate of K % per year.
At the end of the first year, the money in the account is $2036.
(i) Show that K = 1.8.
[2]
(ii) Find the number of complete years before Nicole has at least $2150 in the account.
Show your working.
[3]
8
(a) The price of an electric drill is $78.
In a sale, the price is reduced by 15%.
Calculate the sale price.
[2]
(b) The exchange rate between dollars ($) and euros (€) is $1 = €0.85.
Michael changes $100 to euros.
He buys a clock costing €58.99.
He changes the remaining money back to dollars.
[2]
Calculate the amount, in dollars, he has left.
(c)
ACE SIMPLE
COOL COMPOUND
Simple interest at
2.1% per year
Compound interest at
2% per year
Pietro invests $3500 in the Ace Simple account for 4 years.
Eliana invests $3500 in the Cool Compound account for 4 years.
At the end of the 4 years, who has more money in their account and by how much?
9
[4]
(a) In October, Sara is charged $84.25 for water.
A tax of 8% is added to this amount.
Calculate the total amount Sara is charged for water in October including tax.
[2]
(b) The table shows the rates that Sara is charged for her gas and electricity supply.
She is charged a fixed amount each day plus an amount for each unit used.
Cost for one day
Cost for one unit
Gas
23 cents
4.3 cents
Electricity
28 cents
16 cents
(i) Sara uses a total of 960 units of gas in the 30 days of November.
Calculate the total amount, in dollars, Sara is charged for gas in November.
[2]
(ii) Sara is charged a total of $30.80 for electricity in the 30 days of November.
[3]
Calculate the number of units of electricity she used.
(c) The amount of electricity generated is measured in Gigawatt hours (GWh).
The table shows information about the amount of electricity generated in different countries.
Country
Electricity generated in 2010
(GWh)
Electricity generated in 2016
(GWh)
Australia
2.37 # 105
2.43 # 105
Japan
1.09 # 106
1.03 # 106
Spain
2.91 # 105
2.64 # 105
Turkey
2.03 # 105
2.62 # 105
(i) Calculate how much more electricity was generated in Japan than in Australia in 2016.
Give your answer in standard form.
[1]
(ii) Calculate the percentage increase in electricity generated in Turkey from 2010 to 2016.
[2]
(iii) There was a 4% decrease in the amount of electricity generated in Spain from 2013 to 2016.
Calculate the amount of electricity generated in Spain in 2013.
10
[2]
(a) Jasmine buys a family holiday to India.
Here is some information about the cost.
Flights
$700
Hotel
$1550
Total cost
$2250
(i) In October, Jasmine pays a deposit of 12% of the total cost.
She pays the rest of the total cost in December.
Calculate the amount she pays in December.
[2]
(ii) Find the ratio cost of flights : cost of hotel.
Give your answer in its simplest form.
[2]
(b) Jasmine changes $350 into rupees.
The exchange rate is $1 = 71.6 rupees.
On holiday, she spends 19 500 rupees.
She changes the rest back to dollars at the same exchange rate.
Calculate the amount of money she receives.
Give your answer correct to the nearest cent.
[3]
(c) The table shows the number of tourists and the total tourist spending for some countries in 2016.
Country
Number of tourists
Total spending in dollars
China
5.93 # 10 7
4.44 # 10 10
India
1.46 # 10 7
2.31 # 10 10
Kenya
1.27 # 10 6
1.62 # 10 9
Madagascar
2.93 # 10 5
9.13 # 10 5
(i) Calculate how many more tourists visited India than Kenya in 2016.
Give your answer in standard form.
[1]
(ii) Calculate the average amount spent per tourist in China in 2016.
Give your answer correct to the nearest dollar.
[2]
(iii) From 2014 to 2016, the total amount spent by tourists in Madagascar increased by 23.5%.
Calculate the amount spent by tourists in Madagascar in 2014.
[2]
11
Anton invests $6000 in an account for 5 years.
The account has a compound interest rate of 2.5% per year.
At the end of 5 years, he spends $4200 of this money on a family holiday to Malaysia.
[3]
(a) How much money is left in the account?
(b) Anton changes $800 into Malaysian Ringgits (MYR) for his trip.
The exchange rate is $1 = 3.16 MYR.
He spends 2250 MYR and then changes the remaining money back into dollars ($).
The exchange rate on his return is $1 = 3.27 MYR.
How many dollars does he receive on his return?
Give your answer correct to the nearest dollar.
[3]
(c) Anton invests $1500 in another account.
The account has a compound interest rate of p% per year.
At the end of 3 years, there is $1598.85 in the account.
Calculate p.
Give your answer correct to 2 decimal places.
12
[3]
(a) Stefan had an annual income of $21 500 in 2018.
His annual income increased to $22 790 in 2019.
Calculate the percentage increase.
[2]
(b) Stefan invests $1260 in a bank.
The bank pays simple interest at a rate of 2.5% per year.
[2]
Calculate the amount Stefan has in the bank at the end of 3 years.
(c) Stefan changes 4300 Indian Rupees (INR) into dollars ($).
The exchange rate is $1 = 67.8 INR.
Work out how much he receives.
Give your answer correct to the nearest dollar.
13
[2]
(a) The length of a rectangle is 6 cm more than its width, w cm.
The perimeter of the rectangle is 37 cm.
[3]
Form an equation in w and solve it to find the width of the rectangle.
(b)
28
NOT TO
SCALE
8
15
20
A rectangle 20 cm by 8 cm is cut from a rectangle 28 cm by 15 cm.
Each measurement is given correct to the nearest centimetre.
Calculate the upper bound for the area of the shaded region.
[3]
14
(a) Here is some information about a holiday.
7-night holiday
$340 per person
On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.
[2]
8% discount if you book before 31 March
(b) Naseem hires a car for his holiday.
The total cost is $241.50 .
This cost includes 15% tax.
Calculate the cost of hiring the car excluding tax.
[2]
(c) Naseem drives a total of 800 km on holiday.
He uses a total of 29.6 litres of fuel.
Calculate the average rate of fuel used in litres per 100 km.
[2]
(d) Naseem changes $450 to euros (€) for his holiday.
The exchange rate between dollars and euros is $1 = €0.82 .
On holiday, he spends €297.
Naseem changes the remaining money back to dollars when he returns home.
The exchange rate is now $1 = €0.80 .
Work out how many dollars he receives.
15
[3]
(a) The cash price of a car is $13 000.
Marta pays in instalments for this car.
Marta pays a deposit of 15% of the cash price.
She then pays 24 monthly instalments of $500.
Calculate the total amount Marta pays for the car.
[3]
(b) The price of a phone is reduced by 12% in a sale.
The sale price of the phone is $286.
Calculate the price of the phone before the sale.
[2]
(c) The exchange rate between dollars ($) and pounds (£) is $1 = £0.71 .
The exchange rate between euros (€) and pounds (£) is €1 = £0.87 .
Calculate the exchange rate between dollars and euros.
Give your answer correct to 2 decimal places.
[2]
(d) Samuel invests $1500 in an account paying 1.9% per year compound interest.
Nina invests $1500 in an account paying 1.9% per year simple interest.
They each leave the money in their account for 5 years.
At the end of 5 years, how much more money does Samuel have in his account than Nina has in
hers?
[4]
MARK SCHEME
1(a)(i)
1
2380
3
1(a)(ii)
1
751.1[0]
2
1(b)(i)
85.14
1
1(b)(ii)
1400
3
1(b)(iii)
1.82 or 1.818…
2
28
 5200 oe
100
3
M1 for
 5200 oe
25
M1 for
1.5
 740 oe
100
or B1 for 11.1[0]
M1 for 740 +
M1 for
215.60
soi
2.20
M1 for
their 98
100 oe
7
M1 for
2.24  2.20
100 oe or
2.20
2.24
100 oe
2.20
2(a)(i)
27.8[0] to 28.4[0]
1
2(a)(ii)
2.45 to 2.55
2 B1 for 18.5 soi
2(b)
4.4
2
2(c)
3.7 nfww
3 M2 for 8.8125 = 2.35(d + 0.05) oe
or B2 for answer 3.75
OR
B1 for 2.35 seen
8.8125
M1 for
or
their2.35
8.8125  their 2.35  0.05
oe
for
their 2.35
M1 for
10
11
[11] or
[10]
6  8 11
6  8 11
3(a)i
1638[.00]
1
3(a)(ii)
14.3 or 14.28 to 14.29
2
M1 for
96  84
100 oe or
84
96
 100 [100] oe
84
3(b)
1020 nfww
3
15 

M2 for 1200   1 
 oe
 100 
OR
15
M1 for 1200  96  
 1200  96  oe
100
or B1 for 17280 (cents) or ($)172.8[0]
their 97920
M1 for
oe
96
After 0 scored, SC2 for answer 1020 from
consistent use of figs96
3(c)
10.1[0]
2
3(d)
12.5[0]
2
4(a)
39 [hours] 35 [minutes]
2 B1 for 2375 [min] or 35 [h] 275 [m]
or 7 [h] 55 [m] or 475 [min]
or 22 [h] 5 [m] or 17 [h] 30 [m]
After 0 scored, SC1 for answer 39 [h] 35 [m] to
39 [h] 36 [m]
4(b)
14.91 final answer
2
M1 for 14.20 +
4(c)
8 : 15 : 17 final answer
3
M2 for
M1 for 1.10 
M1 for
3.5 1
oe
0.5
100  7.2
x  13.4[0] soi
100
5
 14.20 oe
100
or B1 for 0.71 seen
1 3 17
k : k : k soi or 20 : 37.5 : 42.5 oe
5 8 40
or for final answer ratio with 8, 15 and 17 in wrong
order
or M1 for
1
3
k + k or 20[%] + 37.5[%] soi
5
8
4(d)
1.6
2
M1 for
2400  r  4
= 153.60 oe
100
4(e)
1700[.00…]
3
M2 for
1822.38
oe
1.0145
5
 1.4 
or M1 for x  1+
 = 1822.38 oe
 100 
5(a)(i)
13 22, 23 01
2 B1 for each
5(a)(ii)
2 [hours] 41 [minutes]
1
5(b)
0.87
3
M2 for
0.75  290
oe
250
or M1 for
290
250
oe seen or
oe seen
250
0.75
or
0.75 250
oe seen
=
r
290
5(c)(i)
252
2
M1 for 420  3 
20
oe
100
or B1 for 84 seen or 252 seen
5(c)(ii)
12.6[0]
3 B2 for answer 100.8[0]
or M2 for
85.68
100
oe

8
100 − 15
or M1 for
100 − 15
x = 85.68 8 soi
100
6(a)
1.56 × 107 cao nfww
3 B2 for 15 600 000 oe or 15 550 000 oe or
15 552 000 oe or
answer (cao) 1.56 × 109 or 1.55 × 107 or
3.11× 108 or 3.11× 106 or 2.59 × 105 or
5.18 × 104 (nfww)
or M1 for 720 × 24 × 60 × 300 × 0.05
6(b)
34
3
B1 for 21.25 and 17.85 seen
M1 for [–](their 21.25 × 10 – their 17.85
× 10) oe
7(a)
32.7 or 32.72 to 32.73
2
7(b)
22 880
2
M1 for
7200
[×100]
22000
M1 for 22000 +
or B1 for 880
7(c)(i)
7(c)(ii)
K 

2000 1 +
 = 2036 soi
 100 
M1
K  2036

leading to K = 1.8
1 +
=
 100  2000
A1
A
5 with
2147 to 2148 and 2186 to 2187
3
A0 for any incorrect working
 1.8 
M2 for [2000] 1 +

 100 
 1.8 
[2000] 1 +

 100 
1.018n = 1.075
or
n
 1.8 
5 with 1 +
 = 1.075 and
 100 
1.073 to 1.074 and 1.093 to 1.094
4
× 22000 oe
100
5
4
oe or
oe or
 1.8 
or M1 for 2000  1+

 100 
n>1
n
2150
 1.8 
1
+

 =
2000
 100 
or
5 with 4.05 or 4.053 to 4.054
8(a)
66.3[0]
2
8(b)
30.6[0]
2
8(c)
Pietro and 5.48 or 5.49
4
n
oe where
15
× 78 oe
100
or B1 for 11.7[0]
M1 for 78 –
M1 for 100 × 0.85 – 58.99 or
M1 for 3500 +
AND
58.99
0.85
3500 × 2.1 × 4
oe
100
2 

M2 for 3500 1 +

 100 
4
2 

or M1 for 3500 1 +

 100 
oe
k
oe where k > 1
4
2 

or after M0, SC1 for 3500 1 +
 + 3500
 100 
9(a)
90.99
2
M1 for 84.25 +
or B1 for 6.74
9(b)(i)
48.18 final answer
8
× 84.25 oe
100
2 M1 for 960 × 4.3 + 30 × 23
or 960 × 0.043 + 30 × 0.23
If 0 scored, SC1 for answer 222.09
9(b)(ii)
140
3 M1 for 3080 – 30 × 28 oe
or 30.8 – 30 × 0.28 oe
M1 for their 2240 ÷ 16 oe
9(c)(i)
7.87 × 105 final answer
1
9(c)(ii)
29.1 or 29.06...
2
9(c)(iii)
275 000 or 2.75 × 105 nfww
2
10(a)(i)
1980
2
2.62 × 105 − 2.03 × 105
[×100] oe
2.03 × 105
2.62 ×105
×100 oe
or for
2.03×105
M1 for
M1 for
(100 − 4 )
100
M1 for 2250 −
or B1 for 270
x = 2.64 × 105 soi
12
× 2250 oe
100
After 0 scored, SC1 for answer 3960
10(a)(ii)
14 : 31 final answer
2 M1 for 700 : 1550 oe
After 0 scored, SC1 for answer 31 : 14
10(b)
77.65 cao
3
M2 for 350 −
19500
oe
71.6
OR
M1 for 350 × 71.6 soi
their 25060 − 19500
M1 for
oe
71.6
10(c)(i)
1.333 × 107 final answer
1
10(c)(ii)
749 or 7.49 × 102 cao
2
10(c)(iii)
739 000 or 7.39 × 105
2
M1 for
M1 for
4.44 ×1010
oe
5.93×107
(100 + 23.5)
100
x = 9.13 × 105 soi
11(a)
2590 or 2588 to 2589
3
2.5 

M2 for 6000 1 +

 100 
5
n
2.5 

or M1 for 6000 1 +
 where n > 1
 100 
After 0, SC1 for answer 2550
11(b)
85 cao
3
M2 for
800 × 3.16 − 2250
3.27
or M1 for 800×3.16 or answer from
11(c)
2.15
3
M2 for 3
x
3.27
1598.85
1500
or M1 for 1500 k 3 = 1598.85 oe
12(a)
6
2
M1 for
22790 − 21500
[×100] oe or
21500
22790
×100 oe
21500
12(b)
1354.5[0]
2
12(c)
63[.00] cao
2
13(a)
w + 6 + w + w + 6 + w = 37 oe
M2 M1 for length = w + 6
6.25
B1
13(b)
295.5
3 B1 for two of 28.5, 15.5, 19.5, 7.5
M1 for their (28.5 × 15.5) – (19.5 × 7.5)
14(a)
625.6[0]
2 M1 for [2 ×] 340 × 0.92 oe
or B1 for 54.4[0] in working
14(b)
210
2
14(c)
3.7
2 B1 for answer figs 37
29.6
×100 oe
or M1 for
800
14(d)
90
3 M1 for 450 × 0.82 soi
[their 369−]297
M1 for
oe
0.80
M1 for [1260 + ]
M1 for
M1 for
3 × 2.5
×1260 oe
100
4300
soi
67.8
100 +15
x = 241.50 soi
100
15(a)
13 950 final answer
3 M1 for 13 000 × 0.15 oe
M1 for 24 × 500 oe
15(b)
325
2
15(c)
0.82
2 B1 for answer 0.81[6…]
0.71
oe
or M1 for
0.87
15(d)
5.51 or 5.52
4
M1 for
100 −12
x = 286 soi
100
5
 1.9 
M2 for 1500 × 1 +
 oe
 100 
k
 1.9 
or M1 for 1500 × 1 +
 oe where k
 100 
>1
or after M0, SC1 for
5
 1.9 
1500 ×  1 +
 +1500
 100 
AND
1500 × 1.9 × 5
+ 1500 oe
M1 for
100